142 Mr. Lubbock on the Calculation of Annuities, and 



the probability of drawing a ball of any given colour calculated 

 from a few observations will be little to be depended on, but it 

 will also differ the more from the ratio of the number of times 

 a ball of the given colour has been drawn, divided by the number 

 of the preceding trials, the fewer the latter have been. 



Laplace {TMor. Anal, des Prohabilites, p. 426.) has in- 

 vestigated the method of determining the value of annuities, he 

 there says, " Si I'on nomrae yo le nombre des individus de Page 

 A dans la table de mortalite dont on fait usage et y, le nombre 

 des individus a I'age A+x la probabilite de payer la rente a la 



fin de 1' annee A + X sera — ," this hypothesis coincides with 



that I have before alluded to, as adopted by all other writers. 

 Laplace, however, means this as an approximation, for he has 

 investigated differently the probability of an individual of the 

 age A living to the age A + a, p. 385 of the same work. He 

 there considers two cases only possible, but as an individual 

 may die at any instant during life, I think it may be doubted 

 whether this hypothesis of possibility should be adopted. 



Captain John Graunt was the first, if I am not mistaken, 

 who directed attention to questions connected with the duration 

 of life, he published a book in 1661, entitled Obsenmtions on 

 the Bills of Mortality ■• which contains many interesting details 

 although it is written in the quaint style which prevailed in 

 those times. In this book, amongst other tables, there is one 

 shewing in 229250 deaths how each arose : and another shewing 

 of 100 births " how many die within six years, how many the 

 next decad, and so for every decad till 76," which is in fact 

 a table of mortality, and is probably the first ever published. 



After Captain Graunt, Sir W. Petty published his Essays 

 on Political Arithmetick; Halley, however, was the first who 



